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Volume 7, Number 10
7 October 2006
Q10004, doi:10.1029/2006GC001274
AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES
Published by AGU and the Geochemical Society
ISSN: 1525-2027
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A study of the relation between ocean storms and the Earth’s
hum
Junkee Rhie and Barbara Romanowicz
Berkeley Seismological Laboratory, University of California, Berkeley, 209 McCone Hall, Berkeley, California 94720,
USA ([email protected]; [email protected])
[1] We previously showed that the Earth’s ‘‘hum’’ is generated primarily in the northern oceans during
the northern hemisphere winter and in the southern oceans during the summer. To gain further insight
into the process that converts ocean storm energy into elastic energy through coupling of ocean waves
with the seafloor, we here investigate a 4-day-long time window in the year 2000 that is free of large
earthquakes but contains two large ‘‘hum’’ events. From a comparison of the time functions of two
events and their relative arrival times at the two arrays in California and Japan, we infer that the
generation of the ‘‘hum’’ events occurs close to shore and comprises three elements: (1) short-period
ocean waves interact nonlinearly to produce infragravity waves as the storm reaches the coast of North
America; (2) infragravity waves interact with the seafloor locally to generate long-period Rayleigh
waves; and (3) some free infragravity wave energy radiates out into the open ocean, propagates across
the north Pacific basin, and couples to the seafloor when it reaches distant coasts northeast of Japan. We
also compare the yearly fluctuations in the amplitudes observed on the two arrays in the low-frequency
‘‘hum’’ band (specifically at 240 s) and in the microseismic band (2–25 s). During the winter, strong
correlation between the amplitude fluctuations in the ‘‘hum’’ and microseismic bands at BDSN is
consistent with a common generation mechanism of both types of seismic noise from nonlinear
interaction of ocean waves near the west coast of North America.
Components: 8173 words, 18 figures, 1 table.
Keywords: Hum of the Earth; microseisms; infragravity waves.
Index Terms: 4546 Oceanography: Physical: Nearshore processes; 4560 Oceanography: Physical: Surface waves and tides
(1222); 7255 Seismology: Surface waves and free oscillations.
Received 9 February 2006; Revised 19 June 2006; Accepted 10 July 2006; Published 7 October 2006.
Rhie, J., and B. Romanowicz (2006), A study of the relation between ocean storms and the Earth’s hum, Geochem. Geophys.
Geosyst., 7, Q10004, doi:10.1029/2006GC001274.
1. Introduction
[2] Since the discovery of the Earth’s ‘‘hum’’
[Nawa et al., 1998], seismologists have tried to
determine the source of the continuous background
free oscillations observed in low-frequency seismic
spectra in the absence of earthquakes.
Copyright 2006 by the American Geophysical Union
[3] In the last decade, some key features of these
background oscillations have been documented.
First, their source needs to be close to the Earth’s
surface, because the fundamental mode is preferentially excited [Nawa et al., 1998; Suda et al.,
1998] and no clear evidence for higher mode
excitation has yet been found. Second, these oscillations must be related to atmospheric processes,
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because annual [Nishida et al., 2000] and seasonal
[Tanimoto and Um, 1999; Ekström, 2001] variations in their amplitudes have been documented.
Finally, they are not related to local atmospheric
variations above a given seismic station, since
correcting for the local barometric pressure fluctuations brings out the free oscillation signal in
the seismic data more strongly [e.g., Roult and
Crawford, 2000].
[4] Early studies proposed that the ‘‘hum’’ could be
due to turbulent atmospheric motions and showed
that such a process could explain the corresponding
energy level, equivalent to a M 5.8–6.0 earthquake
every day [Tanimoto and Um, 1999; Ekström,
2001]. However, no observations of atmospheric
convection at this scale are available to confirm this
hypothesis. In the meantime, it was suggested that
the oceans could play a role [Watada and Masters,
2001; Rhie and Romanowicz, 2003; Tanimoto,
2003].
[5] Until recently, most studies of the ‘‘hum’’ have
considered stacks of low-frequency spectra for
days ‘‘free’’ of large earthquakes. In order to gain
resolution in time and space and determine whether
the sources are distributed uniformly around the
globe, as implied by the atmospheric turbulence
model [e.g., Nishida and Kobayashi, 1999], or else
have their origin in the oceans, it is necessary to
adopt a time domain, propagating wave approach.
In a recent study, using an array stacking method
applied to two regional arrays of seismic stations
equipped with very broadband STS-1 seismometers [Wielandt and Streckeisen, 1982; Wielandt and
Steim, 1986], we showed that the sources of the
"hum" are primarily located in the northern Pacific
Ocean and in the southern oceans during the
northern hemisphere winter and summer, respectively [Rhie and Romanowicz, 2004 (hereafter
referred to as RR04)], following the seasonal
variations in maximum significant wave heights
over the globe, which switch from northern to
southern oceans between winter and summer. We
suggested that the generation of the hum involved a
three stage atmosphere/ocean/seafloor coupling
process: (1) conversion of atmospheric storm energy into short-period ocean waves, (2) nonlinear
interaction of ocean waves producing longerperiod, infragravity waves, and (3) coupling of
infragravity waves to the seafloor, through a process involving irregularities in the ocean floor
topography. However, the resolution of our study
did not allow us to more specifically determine
whether the generation of seismic waves occurred
in the middle of ocean basins or close to shore [e.g.,
Webb et al., 1991; Webb, 1998]. The preferential
location of the sources of the Earth’s ‘‘hum’’ in the
oceans has now been confirmed independently
[Nishida and Fukao, 2004; Ekström and Ekström,
2005]. In a recent study, Tanimoto [2005] showed
that the characteristic shape and level of the lowfrequency background noise spectrum could be
reproduced if the generation process involved the
action of ocean infragravity waves on the ocean
floor, and suggested that typically, the area involved
in the coupling to the ocean floor need not be larger
than about 100 100 km2. However, the linear
process proposed may not be physically plausible,
because of the difference in wavelength between
infragravity and elastic waves (S. Webb, personal
communication, 2006).
[6] On the other hand, oceanographers have long
studied the relation between infragravity waves and
swell. Early studies have documented strong correlation between their energy levels, which indicate
that infragravity waves are driven by swell [e.g.,
Munk, 1949; Tucker, 1950]. Theoretical studies
have demonstrated that infragravity waves are
second order forced waves excited by nonlinear
difference frequency interactions of pairs of swell
components [Hasselmann, 1962; Longuet-Higgins
and Stewart, 1962]. A question that generated
some debate was whether the observed infragravity
waves away from the coast are ‘‘forced’’ waves
bound to the short carrier ocean surface waves and
traveling with their group velocity, or ‘‘free’’ waves
released in the surf zone and subsequently reflected
from the beach which, under certain conditions,
may radiate into deep ocean basins [e.g., Sutton et
al., 1965; Webb et al., 1991; Okihiro et al., 1992;
Herbers et al., 1994, 1995a, 1995b]. In particular,
Webb et al. [1991] found that infragravity wave
energy observed on the seafloor away from the
coast was correlated not with the local swell wave
energy but with swell energy averaged over all
coastlines within the line of sight of their experimental sites, in the north Atlantic Ocean and offshore southern California.
[7] Recently, we analyzed the relation between
ocean storms off-shore California and infragravity
wave noise observed on several broadband seafloor
stations in California and Oregon [Dolenc et al.,
2005a]. We also found that the seismic noise
observed in the infragravity wave band correlates
with significant wave height as recorded on regional ocean buoys, and marks the passage of the
storms over the buoy which is closest to the shore.
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Figure 1. (a) Maximum stack amplitude (MSA, see definition in text) filtered using a Gaussian filter with center
period of 100 s for BDSN (blue) and F-net (red), normalized by minimum value of MSA for a given time window.
The linear scale on the y axis to the right is used for the normalized MSA to more clearly see the variations in
amplitude of the background noise. Black dots represent earthquakes which occurred during the period considered.
The corresponding scale is logarithmic (moment magnitude) and is given on the y axis to the left. (b – d) Same as
Figure 1a for 150, 200, and 240 s.
More recent results based on data from an ocean
floor station further away from shore [Dolenc et
al., 2005b] indicate that the increase in amplitude
in the infragravity frequency band (50– 200 s)
associated with the passage of a storm occurs when
the storm reaches the near coastal buoys, and not
earlier, when the storm passes over the seismic
station. This implies that pressure fluctuations in
the ocean during the passage of the storm above the
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Table 1. Mw > 5.0 Earthquake Catalog From 25 January to 9 February in 2000 From NEIC
Date
Time
2000/01/25
2000/01/26
2000/01/26
2000/01/26
2000/01/26
2000/01/27
2000/01/27
2000/01/28
2000/01/28
2000/01/28
2000/01/28
2000/01/28
2000/01/28
2000/01/28
2000/01/29
2000/01/29
2000/01/29
2000/01/31
2000/02/01
2000/02/01
2000/02/02
2000/02/02
2000/02/02
2000/02/03
2000/02/03
2000/02/03
2000/02/04
2000/01/25
2000/02/06
2000/02/06
2000/02/07
2000/02/07
2000/02/08
2000/02/09
2000/02/09
2000/02/09
16:43:22.95
13:26:50.00
21:37:57.77
23:00:19.94
23:34:04.50
02:49:44.91
10:10:57.25
08:49:30.87
13:17:52.87
14:21:07.34
16:39:24.28
17:57:00.55
22:42:26.25
22:57:51.70
02:53:54.89
05:48:10.77
08:13:10.73
07:25:59.74
00:01:05.42
02:00:10.68
12:25:21.92
21:58:49.71
22:58:01.55
10:24:57.77
13:42:25.04
15:53:12.96
07:02:11.39
16:43:22.95
02:08:07.14
11:33:52.28
06:34:49.67
16:41:04.58
18:01:27.18
04:28:00.48
09:33:54.05
18:40:37.83
Latitude
27.6630
17.2720
30.9730
40.0210
23.7220
34.8070
31.6780
7.4570
7.4850
43.0460
26.0760
14.4350
1.3470
9.6910
4.8570
20.5630
8.6330
38.1140
4.3580
13.0100
49.0240
5.7300
35.2880
65.0087
13.5720
75.2710
40.6310
27.6630
1.2950
5.8440
43.3680
31.0370
21.9360
16.6660
30.1050
27.6220
station can be ruled out as the direct cause of the
low-frequency seismic noise.
[8] In this paper, we investigate these processes
further in an attempt to better understand where the
coupling between infragravity waves and ocean
floor occurs, generating the seismic ‘‘hum.’’ In
particular, we describe in detail observations made
during one particular time period of unusually high
levels of low-frequency noise. We also present
comparisons of the observed low-frequency seismic ‘‘hum’’ with noise in the microseismic frequency band (2–25 s), and discuss the relation
between the two phenomena.
2. Earthquake ‘‘Free’’
Interval 2000.031–034
[9] In our previous study [RR04], we extracted
time intervals which were not contaminated by
Longitude
Depth
Mag.
92.6310
174.0020
95.5020
52.9010
66.4770
105.4590
141.6860
77.8500
122.6780
146.8370
124.4960
146.4620
89.0830
118.7640
126.2590
178.2880
111.1370
88.6040
151.9070
88.8470
124.9790
148.9320
58.2180
154.2390
121.5460
10.1950
85.9180
92.6310
126.2720
150.8760
147.4330
141.6940
170.0680
172.6960
178.1130
65.7240
33.0
33.00
33.00
33.00
221.60
10.00
33.00
21.40
574.90
61.10
193.90
45.20
10.00
83.40
100.00
562.90
60.70
33.00
189.00
55.00
10.00
112.80
33.00
10.00
33.00
10.00
10.00
33.0
33.00
33.00
61.50
33.00
33.00
33.00
56.70
10.00
5.20
6.30
5.20
5.30
5.00
5.40
5.30
5.40
5.50
6.80
6.00
5.20
5.50
5.60
5.10
5.00
5.40
5.40
5.20
5.20
5.40
5.30
5.30
5.98
5.50
5.50
5.30
5.20
5.50
6.60
5.20
5.40
5.40
5.20
5.00
5.10
earthquakes, using strict selection criteria based
on event magnitude. This significantly limited the
number of usable days in a given year. For example,
only 64 days of ‘‘earthquake free’’ data were kept
for the year 2000. Among these, we identified the
time interval 2000.030 to 2000.034 (i.e., 30 January
to 3 February) as a particularly long interval free of
large earthquakes, during which the background
noise amplitude was unusually high, and during
which two large noise events were observed, that
could be studied in more detail.
[10] As described in RR04, we considered data at
two regional arrays of very broadband seismometers, BDSN (Berkeley Digital Seismic Network) in
California, and F-net in Japan. For each array, we
stacked narrow-band filtered time domain vertical
component seismograms according to the dispersion and attenuation of Rayleigh waves, assuming
plane wave propagation from an arbitrary azimuth.
Here, we apply a 6 hour running average with a
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Figure 2. (a) Mean stack amplitude averaged over 6 hour sliding window (window shifted 1 hour between
resolutions) as a function of time and back azimuth for F-net. A Gaussian filter with center period of 150 s was
applied before stacking. (b) Same as Figure 2a for BDSN. (c) Same as Figure 2a for center period of 240 s. (d) Same
as Figure 2c for BDSN. The time difference between corresponding energy arrivals at the two arrays on day 31 is
about 8 – 10 hours, with F-net lagging behind BDSN. This is more clearly seen in the shorter-period plot.
time step of 1 hour to the stacked data at BDSN
and F-net respectively. At each time step, the stack
amplitude has a maximum corresponding to a
particular back-azimuth. We consider the resulting
maximum stack amplitudes (MSA) as a function of
time. We show in Appendix A that the level of the
background ‘‘hum’’ is consistent with previous
estimates [e.g., Tanimoto and Um, 1999; Ekström,
2001].
[11] We consider the 15 day period 2000.25 to
2000.40. In Figure 1, we plot the MSA as a
function of time in four different period bands.
We here use a linear scale for the MSA (different
from Figure A1) to more clearly see the variations
in amplitude of the background noise. We note the
well defined signature of large earthquakes, which
have a sharp onset, a slower decay and a relatively
sharp end. At the time resolution considered here,
this onset is practically coincident at both arrays.
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Figure 3. Same as Figure 1 for days from 340 to 355 in 2002.
The duration of the earthquake signal increases
with the size of the earthquake and is typically on
the order of 0.5 day for Mw 6 and 1–1.5 day for
Mw 7 earthquakes, after which the signal drops
below the average background noise level. This is
consistent with what one expects from the decay of
Earth circling mantle Rayleigh waves generated by
large earthquakes.
[12] Table 1 lists all earthquakes larger than M 5.0
during these 15 days, as reported in the NEIC
catalog. During the time interval 2000.031 to
2000.034, there are no earthquakes larger than
M 5.5, yet the background noise rises well above
the noise floor, forming two particularly long
events, with a very different signature from that of
earthquakes: the rise time is longer, the decay very
slow and the ratio of the duration of each event to its
maximum amplitude, significantly larger. These
two noise events are observed on both arrays (i.e.,
in California and in Japan), and there is a lag time of
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Figure 4. (a) Results of grid search method to locate the source of continuous long-period Rayleigh waves on
31 January 2000. Six hour waveforms Gaussian filtered with center period of 100 s from F-net, BDSN, and
10 European stations are used. Color indicates the mean stack amplitude over a 6 hour time window
(2000.031,14:00– 2000.031,20:00 UTC) after correcting waveforms at individual stations for attenuation and
dispersion. (b) Same as Figure 4a for 150 s.
several hours between the two arrays. The second
event is weaker at the longest periods. We verify
that the back-azimuth corresponding to the maximum amplitude is very stable during these two
events, as illustrated in Figure 2, which also emphasizes the delay of about 8–10 hours between the
main energy arrivals at BDSN and F-net. We will
discuss these events in detail in what follows.
[13] This particular ‘‘earthquake free window’’ is
unique in that it lasts several days, and the noise
events are large. However, noise events with similar characteristics are observed at other times as
well. For example, Figure 3 shows a similar plot
for the time period 2002.340 to 2002.355, in which
we observe a noise event beginning on day
2002.349, showing similar time evolution as for
the events in 2000 described above: a slow rise
time and lag of 8–10 hours between the two
arrays. It is followed by a second noise event of
similar characteristics, but partially hidden behind
an earthquake of Mw > 6. In what follows, we
return to the time period 2000.031–034 for further
analysis.
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Figure 5. (a) Locations of five quiet seismic stations in North America. (b) Power spectral density (PSD) at CMB. It is
clear that two large seismic energy arrivals (highlighted with black circles) are present on days 031 and 033. (c –f) Same as
Figure 5b for TUC, ANMO, CCM, and HRV, respectively. For CCM the data are missing after day 33 through day 35. Large
amplitude signals for periods <120 s on days 34 and 35 correspond to earthquakes (see Table 1).
[14] The large noise events observed on days
2000.031 and 2000.033 after applying a smoothing
moving average to the MSA, are the coalescence of
multiple smaller events, which, as we showed
previously, propagate across the two arrays with
the dispersion characteristics of Rayleigh waves
(see Figure 1 in RR04). In order to locate the
sources of these disturbances in RR04, we applied
a back-projection grid-search method to the original time series, after band-pass filtering between
150–500 s, over a 6 hour period containing the
maximum stack amplitude on day 2000.031. We
showed that the sources of Rayleigh waves that
best fit the amplitudes observed both at BDSN and
F-net are located in the North Pacific Ocean basin.
We here apply the same back-projection method,
but using a narrow band filter centered at 150 and
100 s respectively, and obtain a band of source
locations which follows the north Pacific shoreline,
as illustrated in Figure 4. This is particularly clear
at 100 s.
[15] In order to obtain a stable solution using the
grid search method, it is necessary to process a
time interval of length about 6 hours, indicating
that many of the small events which compose the
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Figure 6. (a) Mean amplitude estimates and corresponding errors at stations considered in Figure 5. Error is
estimated by random perturbation of time (±6 hour) and period (±30 s) window used for averaging. (b) Normalized
observed mean amplitudes (black dots) and the theoretical attenuation curve (red) for the seismic source location
indicated by a circle in Figure 6c. Gray shaded region and horizontal blue bars indicate the possible range of
theoretical attenuation curves and epicenters from stations to possible source locations giving the good fit (i.e.,
normalized inverse misfit >0.7). (c) Results of grid search for the location of the source of PSD noise highlighted in
Figure 5. The PSD amplitudes were corrected for attenuation and geometrical spreading. The color scale represents
the normalized inverse of the misfit between observed and predicted amplitudes (this way, the minimum misfit is
always equal to 1). The circle indicates the off-shore location with small misfit.
larger noise event on day 2000.031 are too small to
be studied individually, at least with this method:
the minimum duration of the time window necessary to obtain a stable result is controlled by the
available signal/noise ratio in the stacks. Here we
show that the large ‘‘composite’’ event, obtained
when using the 6 hour moving average, propagates
west to east across the whole North American
continent, with an amplitude decay consistent with
the propagation of Rayleigh waves. Instead of
stacking the noise data over an array of broadband
seismic stations, we here consider five quiet
broadband stations in North America, and, for
each of them, we compute power spectral density
(PSD) as a function of time, with a 6 hour moving
window and a 1 hour lag (Figure 5). All five
stations show an increase in background noise
during days 31–32, and another one, with smaller
amplitude and narrower frequency range, on day 33
(except for CCM for which data are not available on
that day). Figure 6a compares the mean Fourier
amplitudes at stations CMB, TUC, ANMO and
HRV, averaged over the period range 100–200 s
and time range 2000.31,00:00 and 2000.32,06:00.
We chose this period range, because at lower
frequencies, the background noise is dominated
by site effects at some of the stations. From the
amplitude decay it is possible to obtain a very rough
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Figure 7. (a) Location of the two seismic arrays (blue squares) and ocean buoys (green dots). (b) Significant wave
height recorded at buoy 21004. (c – e) Same as Figure 7b for buoys 44059, 46027, and 46026. (f) Maximum stack
amplitude (MSA) Gaussian filtered with center period of 240 s recorded at F-net. (g) Same as Figure 7f for BDSN.
Peaks in ocean wave data at off-shore buoys (21004 and 46059) arrive earlier than seismic peaks. For BDSN, arrival
times of seismic energy are closer to those of the ocean wave peaks at buoys near the coast (46027 and 46026). The
events arrive latest on F-net. Note that the MSA is also lower at F-net than at BDSN, consistent with more distant
sources.
estimate of the location of the source of Rayleigh
waves by forward amplitude modeling. The results
are shown in Figure 6c, using CMB, TUC, ANMO
and HRV. Because the available azimuth range is
not very wide, there is a large uncertainty in the
longitude of the inferred source. However, it is
compatible with a location near the west coast of
North America. Figure 6b compares the observed
and predicted average Fourier amplitudes at four
stations. The amplitudes are normalized to those of
the most western station (CMB) and the predicted
amplitudes are computed assuming the Q model of
PREM for Rayleigh waves [Dziewonski and
Anderson, 1981] and accounting for geometric
spreading.
3. Correlation With Ocean Buoy Data
[16] To further investigate the origin of the noise
events on days 2000.031 and 2000.033, we now
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Figure 8. Significant wave height map on 31 January
2000 for the north Pacific Ocean, based on
WAVEWATCH III. (a – d) Different time windows from
0 to 18 hour with 6 hour interval.
turn to a comparison with ocean buoy data. We
collected significant wave height (SWH) data measured at buoys deployed in the north Pacific by the
National Ocean and Atmospheric Administration
(NOAA) and the Japan Meteorological Agency
(JMA) and operational during those days. We
compare SWH time series for this time period to
the time evolution of the maximum stack amplitudes at BDSN and F-net for the same time
interval. Figure 7 shows such a comparison for
buoys located near Japan and near the California
coast. The time series on all buoys closely resemble the ‘‘source signature’’ on the seismic stacks,
shown here at a period of 240 s. This is the case for
the event on 2000.031 as well as for the smaller
one on 2000.033. The seismic noise events on
BDSN lag those observed on buoy 46059 by about
10–12 hours, but are more or less coincident (to
within 1 hour, which is the minimum resolution of
these plots) with the events observed on the near
shore buoys, indicating that the location of the
coupling between ocean waves and the seafloor
occurs somewhere between buoy 46059 and the
shore, which is consistent with the results of
Figure 6c. The ocean storm which generated the
short-period waves observed on buoys both near
Japan and near the western US moved from east
to west across the north Pacific basin. Unfortunately, we could not find any buoy data closer to
the eastern coast of Japan, or in other parts of the
western Pacific Ocean. To further investigate the
source of these waves, we therefore turn to wave
models. Figure 8 shows snapshots of the evolution of wave height in the northern Pacific for
day 2000.031, from the WAVEWATCH III model
[Tolman, 1999]. During that day, a large storm
arrives from the west toward the coast of California and Oregon. It reaches the coast, according
to the model, between 6h and 12h on day
2000.031. It is followed by a smaller ‘‘tail,’’ about
3000 km behind, which, in turn, according to the
WAVEWATCH III model, reaches the coast between 0h and 6h on day 2000.033 (not shown).
The following storm system, which forms in the
western part of the north Pacific (around longitude 160°E on Figure 8) on day 2000.031 develops into a stronger storm over the next few days.
This can be seen in the animation provided by
NOAA at http://ursus-marinus.ncep.noaa.gov/
history/waves/nww3.hs.anim.200001.gif and
http://ursus-marinus.ncep.noaa.gov/history/waves/
nww3.hs.anim.200002.gif. This storm is not associated with any significantly increased seismic
noise on BDSN or F-net (Figure 1). Notably however, in contrast to the previous one, this storm does
not reach the California coast, but dissipates in the
middle of the ocean. The distribution of wave
heights on Figure 8, together with the observation
of the significant delay in the stack energy at F-net
with respect to the BDSN (see also Figure 2), leads
us to propose the following sequence of events.
[17] On day 2000.031, a large storm, which developed two days earlier in the middle of the north
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Figure 9. A schematic plot of the mechanism of conversion of energy from storm-related ocean surface waves to
seismic waves. Gray circle indicates the moving storm, and blue and red circles (arrows) represent the source regions
(radiation) of infragravity and seismic waves, respectively.
Pacific basin (according to wave models and buoy
data) and moving eastward toward North America,
reaches the vicinity of the western United States
coast. A second storm, weaker, but with similar
characteristics, follows by about 2 days. The seismic background noise observed on the BDSN and
F-net arrays has the same amplitude signature, as a
function of time, as the storms. The process that
converts the storm energy into seismic energy,
which then propagates as Rayleigh waves, in
particular through the North American continent,
appears to involve several steps (Figure 9): when
the storm approaches the US coast with its rough
seafloor topography, short-period ocean waves interact nonlinearly to produce infragravity waves.
Part of the infragravity wave energy then converts to
seismic waves locally, to produce the background
noise event observed on BDSN, and part is
reflected back out to the ocean and travels across
the Pacific basin, in agreement with oceanographic
studies of the generation of infragravity waves [e.g.,
Munk et al., 1964; Elgar et al., 1992; Herbers et al.,
1995a, 1995b]. We estimate that, at 220 m/s,
‘‘free’’ infragravity waves propagate about 6000–
8000 km in 8–10 hours. Consistent with the backazimuth of the maximum arrival of energy, the
conversion from infragravity waves to seismic
waves detected on F-net primarily occurs in the
vicinity of the western Aleutian arc. We note that
the absolute level of MSA is larger at BDSN than at
F-net (e.g., Figures 2 and 7), in agreement with the
inference that the source for F-net should be comparatively more distant and also weaker.
[18] We infer that free infragravity waves play a
role in generating the seismic disturbances in Japan
because of the 8–10 hour time delay between stack
maxima on BDSN and F-net. This is consistent
with observations of remotely generated infragravity waves [e.g., Herbers et al., 1995a]. This time
delay is too short for propagation of short-period
ocean waves (and also ‘‘bound’’ infragravity
waves) from the center of the north Pacific basin,
and much too long for propagation of seismic
waves from a source near the US coast to Japan.
An alternative scenario for the sources of seismic
noise on F-net could involve the storm which
forms on the Japan side of the Pacific in the middle
of day 2000.031 (Figure 8). However, we rule this
out, because this storm intensifies only later and
reaches its peak around 03h on day 2000.032,
which is much later than the long-period seismic
peak on F-net.
[19] We note that the generation of large infragravity waves from short-period ocean waves along the
east coast of the pacific (Canada, US) rather than
the west coast (Japan) is due to the fact that
prevailing winds are westerlies, and therefore most
ocean waves are driven from the west to the east,
interacting nonlinearly only with the coasts on the
east side of ocean basins.
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of generation of seismic waves is particularly high
for these storms, due to their direction of approach
to the North American coast, and the fact that these
storms actually reach the coast. This is why we can
observe these remarkable ‘‘noise events’’ on the
stacks at BDSN and F-net so clearly. We have
evidence of directionality of the process, in that
station COL (Alaska) does not show any increase
of seismic noise in the 70–250 s pass band during
the same time period. At least, it is below detection
level by our methodology involving PSD spectra,
even though there is an indication, from the noise
in the microseismic bandpass (2–25 s) of a storm
reaching the Alaska coast nearby at the end of day
2000.031 (Figure 11). Such directionality would
also explain why we can so clearly follow the
particular seismic disturbance on day 2000.031
across North America.
[21] Other north Pacific storms must also generate long-period seismic noise, however, the
corresponding noise ‘‘events’’ cannot often be identified as clearly because they are either hidden
behind large seismic events, or do not have sufficient
amplitude levels to rise above the average noise level
on the two seismic arrays considered. We note that
many winter storms never reach the north American
coast, or turn further north into the Gulf of Alaska. A
systematic analysis of storm characteristics in the
north Pacific in relation to the ‘‘hum’’ is beyond the
scope of this paper and will be addressed in a further
study.
4. Comparison With Microseisms
[22] We have shown that infragravity waves generated by winter storms in the north Pacific Ocean
contribute to the source of the low-frequency
‘‘hum’’ events observed in California and Japan.
Figure 10. Significant wave height map on
15 December 2002 based on WAVEWATCH III. (a – d)
Different time windows from 0 to 18 hour with 6 hour
interval.
[20] In summary, the seismic sources that form the
composite events on days 2000.031 and 2000.033
are distributed around the Pacific, both in time and
space, but have a common cause: a strong storm
system which ‘‘hits’’ the North American coast
broadside. A similar type of storm which reaches
North America from the west, occurs on day
2002.349 (Figure 10), causing the disturbances
observed on Figure 3. We infer that the efficiency
[23] The nonlinear wave interactions that give rise
to infragravity waves are also responsible for the
generation of double-frequency microseisms [e.g.,
Hasselmann, 1962, 1963; Longuet-Higgins, 1950],
which are themselves correlated with the wind
wave spectrum [e.g., Babcock et al., 1994; Webb
and Cox, 1986; Bromirski and Duennebier, 2002],
and are known to be generated primarily locally
near the coast [e.g., Haubrich and McCamy, 1969;
Webb, 1998; Bromirski et al., 2005].
[24] Therefore we next investigate the relationship
between microseisms, ocean storms and the lowfrequency ‘‘hum.’’ Even though there are two types
of microseisms, primary (at periods lower than 10 s)
and secondary, or ‘‘double-frequency,’’ at periods
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Figure 11. (a) Power spectral density (PSD) at COLA in Alaska. (b) Mean Fourier amplitude in the period
range 2 – 25 s for COLA.
around 6–8 s [e.g., Friedrich et al., 1998], and
their generation mechanisms are different [e.g.,
Hasselmann, 1963; Webb, 1998], the doublefrequency microseisms dominate the spectra and
we will only consider those in the discussion that
follows.
[25] We first computed mean Fourier amplitudes in
the microseismic period band (2 to 25 s) at individual stations of BDSN and F-net for the time
interval 2000.031 – 2000.035. We used moving
windows of duration 30 mn, shifted by 10 mn.
We removed mean and trend before computing
Fourier amplitudes. We then compared them to
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Figure 12. (a) Location map of BDSN and TerraScope stations (black triangle and blue squares) and buoys
(green dots). Blue squares are seismic stations closest to the corresponding buoys. (b – d) Significant wave heights
measured at buoy 46027, 46026, and 46052, respectively. (e – g) Mean Fourier amplitude (count/Hz) over the
period range 2 – 25 s for YBH, BKS, and ISA.
near-by buoy data (Figures 12 and 13). Along the
coast of California (Figure 12), the mean seismic
amplitudes show the signatures of the two noise
events already discussed at low frequency (on days
2000.031 and 2000.033), which are also well
defined on the buoy data. The eastward moving
storm arrives first in northern and central California, as seen by the slight delay in its wave height
signature at buoy 46062 compared to the other two
buoys (see also the data from buoy 46059 on
Figure 7). The timing of the peak of microseismic
noise at the three stations and the fact that the
amplitude at station ISA is smaller by about a
factor of 3 than at BKS, indicate that the generation
of the microseisms occurs closer to the central and
northern California buoys.
[26] Unfortunately, only data for three buoys are
available around Japan for this time period. However, we note that the mean microseismic Fourier
amplitudes at the three seismic broadband stations
closest to the buoys show a good correlation with
SWH data (Figure 13). We also note that, contrary
to the observations in California, the timing and
shape of the microseismic amplitude variations is
different from that at ‘‘hum’’ frequencies, and
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Figure 13. (a) Same as Figure 12 for F-net. (b – d) Same as Figures 12b, 12c, and 12d for 21002, 21004, and 22001,
respectively. (e– g) Same as Figures 12e, 12f, and 12g for ISI, TKD, and AMM.
varies significantly with location of the station in
the array (Figure 14), indicating that, in Japan, the
sources of the microseismic noise and of the hum
are distinct: the low-frequency noise is related to
that observed on the eastern side of the Pacific
(with a delay which we attribute to the propagation
of infragravity waves across part of the Pacific
Ocean), whereas the microseismic noise maximum
occurs significantly earlier (on day 2000.030). In
fact, the time histories of microseism energy at
stations within Japan differ and presumably depend
on the location of each site relative to each storm
track.
[27] To further investigate the relation between
microseismic noise and the low-frequency hum,
we need to be able to compare amplitude levels in
the two frequency bands for long time intervals
(e.g., a whole year). To do so effectively, we
developed a data processing method that avoids
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Figure 14. (top) Location map of seismic stations grouped by their locations in F-net. Different colors indicate
different grouping. (bottom) Mean Fourier amplitude (count/Hz) over the period range 2 – 25 s for two selected
stations in each group shown on the map at the top in black (left column), in blue (center column), and in red (right
column). The variations in amplitude for all five stations (three of them are not shown) in the same group show
similar overall trends.
eliminating the numerous time windows that are
contaminated by earthquakes.
[28] Removing the effect of earthquakes at low
frequencies is difficult to do precisely, due to the
presence of lateral heterogeneity in the Earth and
the relatively low attenuation. In order to minimize
their effects, we compute the minimum value, as a
function of time, in a sliding 1.5 day interval, of the
scaled MSA time series, using a moving time
window with a 6 hour shift. This effectively
removes some large amplitude peaks due to earth17 of 23
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Figure 15. (a) Scaled long-period MSA, Gaussian filtered with center period of 240 s (black curves) for BDSN.
Circles indicate earthquakes. (b) Black curve: same as in Figure 15a. Green curve: minimum obtained after applying
moving time window with duration of 1.5 days and 6 hour shift. (c) Green curve: same as in Figure 15b. Blue curve:
after low-pass filtering with corner period of 1 day. (d) Mean Fourier amplitude over the microseismic band (2– 25 s)
averaged over 7 BDSN stations (black curve). Dots are earthquakes as in Figure 15a. (e) Black curve: same as in
Figure 15d. Green curve: after removing large gradient peaks. (f) Green curve: same as in Figure 15e. Red curve:
low-pass filtered with corner period of 1 day.
quakes, but not all. We then apply a low-pass filter
with a corner period of 1 day to the time series
obtained in the previous step. This further removes
most of the earthquake-related peaks, except for
those with the longest duration, corresponding to
the largest earthquakes (Figures 15a, 15b, and 15c).
We also compute the mean Fourier amplitude in the
microseismic band (2 – 25 s) for seven BDSN
stations. Here the contamination by large earthquakes is not as severe and we only remove those
points which correspond to large temporal gradients. To do so, we empirically determined a
gradient threshold between two consecutive points
in the amplitude time series: if the measured
gradient is higher than the threshold, we remove
the end point and test the gradient value for
successive end points, until the gradient drops
below the threshold. Finally, we low-pass filter
the amplitude time series with a corner period of
1 day (Figures 15d, 15e, and 15f). This effectively
removes most of the earthquake signals.
[29] We compare the filtered ‘‘hum’’ and microseism amplitude time series over a period of one
year, for each array. In the case of California
(BDSN), the level of low-frequency noise does
not vary systematically with time (Figure 16a), but
there is a seasonal variation in the microseismic
amplitude, with a minimum during northern hemisphere summer time, as is also seen in the ocean
wave height data (Figure 16b). This indicates that
the sources of energy for the long-period and shortperiod noise are different during the summer. The
variation in microseismic amplitude at BDSN stations is clearly related with ocean wave height
measured by local buoys (Figure 16b). We can
see a similar trend for F-net, but the correlation of
the variation in short-period amplitudes and ocean
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northern hemisphere winter (January to March and
October to December), we compute the correlation
coefficients between the low-frequency and highfrequency filtered noise time series, for three consecutive years, at BDSN. Correlation coefficients
are significant, between 0.39 and 0.60 (Figure 17).
This indicates that in the winter, both the lowfrequency hum and the microseismic noise observed at BDSN are generated locally. On the other
hand, the corresponding correlation coefficients
for F-net are generally much lower: for the first
3 months of each year, respectively: 0.11, (N/A)
and 0.21; for the last 3 months of each year, respectively: 0.22, 0.02, 0.30.
[31] The correlation between the hum and microseismic noise at BDSN during the winter is compatible with a common generation mechanism for
both types of seismic noise, involving nonlinear
interactions between surface ocean waves giving
rise, on the one hand, to double-frequency microseisms, and on the other, to infragravity waves
[e.g., Hasselmann, 1962]. The fact that the correlation is somewhat weaker at F-net is in agreement
with our proposed scenario, in which the dominant
effect is that of storms moving from West to East
across the Pacific and reaching the west coast of
North America to produce low-frequency seismic
‘‘hum.’’
5. Conclusions
Figure 16. (a) Scaled long-period MSA (red) and
short-period Fourier amplitude (blue), preprocessed as
shown in Figure 15, for BDSN. The short-period mean
Fourier amplitude was computed from 7 BDSN stations
(BKS, CMB, MHC, MOD, ORV, WDC, and YBH).
(b) Preprocessed short-period mean Fourier amplitudes
(blue) for BDSN and significant wave height measured
at buoy 46026 (green). The correlation coefficient
between the two curves is 0.81. (c) Same as Figure 16a
for 5 F-net stations near the eastern coast of Japan
(AMM, ISI, NMR, TKD, and TMR). (d) Same as
Figure 16b for F-net. Significant wave height data
measured at buoy 21004 (green) is not available after
day 190 in 2000. Large peaks in short-period mean
Fourier amplitude and ocean waves during summer
may be coming from the typhoon. The correlation
coefficient between the two curves for the first part of
the year is 0.58.
wave data is weaker than in the case of BDSN
(Figures 16c and 16d).
[30] Removing the time periods contaminated by
the largest events, and restricting our analysis to
[32] We have made progress in clarifying the
mechanism of generation of continuous free oscillations, based on the observations for a time
interval free of earthquakes during which two large
long-period noise events are present in the MSA at
BDSN and F-net. We have shown that these events
can be related to a particular winter storm system.
[33] A perturbation in the atmosphere, typically a
winter storm moving eastward across the north
Pacific basin, generates short-period ocean waves.
As the storm reaches the north-American coast, the
nonlinear interaction between ocean waves generates long-period infragravity waves, some of which
convert locally to long-period seismic energy, and
others propagate long distance across the ocean
basin and couple to the seafloor near northeastern
coasts. The resulting long-period seismic waves
propagate over the globe and give rise to the
‘‘hum.’’ In particular, we were able to track the
seismic energy generated off-shore California by
the storm considered on day 2000.031, throughout
the North American continent.
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Figure 17. (a) Comparison between preprocessed scaled long-period MSA (red) and short-period mean Fourier
amplitudes (blue) for the first three months of 2000. Time windows strongly contaminated by earthquakes are shaded
in gray. Corresponding correlation coefficient is shown in the plot. (b) Same as Figure 17a for the last three months in
2000. (c – d) Same as Figures 17a and 17b for 2001. For Figure 17c, correlation coefficient is not computed because
of significant contamination from earthquakes throughout the time period considered. (e – f) Same as Figures 17a and
17b for 2002.
[34] The directionality of the ‘‘hum’’ radiation suggested by our data needs to be further characterized,
in particular for the benefit of studies of structure
based on the analysis of noise cross-correlations
[e.g., Shapiro et al., 2005], at least at low frequencies. Indeed, the sources of low-frequency seismic
noise can no longer be considered as uniformly
distributed either in time, or in space.
[35] The annual fluctuations of long- (hum band)
and short- (microseism band) period seismic amplitudes at BDSN and F-net show quite different
features. We can clearly see the seasonal change
in amplitude in the microseism band (2–25 s) with
a minimum during northern hemisphere summer,
whereas the amplitude in the hum band (here
considered at 240s) does not show clear seasonal
variations. We also observed a significant correlation between seismic amplitudes at BDSN in the
microseism and hum bands during northern hemisphere winter. We had previously documented that
the source of the hum observed at BDSN and F-net
shifts from the northern Pacific to the southern
oceans between winter and summer, so that the
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Figure A1. Estimation of the level of low-frequency background noise at 240 s (i.e., the hum) for the year 2000.
(a) Moment magnitudes versus associated maxima in MSA for BDSN. The MSA is shown after applying a moving
average over a window of 6 hours with 1 hour offset. Results do not significantly change if no moving average is
applied. Black dots indicate all seismic events during the year, and solid squares indicate selected maxima which are
not contaminated by later Rayleigh wave trains from other large events. The best fitting line is computed using only
the data indicated by blue squares. The best fitting line is used to scale MSA to match the plausible level of the back
ground noise. (b) Same as Figure A1a for F-net. Red squares are selected maxima. (c) Scaled MSA (blue) for BDSN.
Open circles represent all large events during the year 2000. The levels corresponding to Mw 5.75 and Mw 6 are
highlighted with green lines. (d) Same as Figure A1c for F-net (red).
sources are more ‘‘local’’ in the winter than in the
summer. In contrast, microseisms propagate less
efficiently at large distances, so the source is
primarily local. These observations are in agreement with a common mechanism for the simultaneous generation of short- and long-period seismic
noise near the California coast, as inferred from
theoretical studies.
Appendix A
[36] We estimate the background level of the lowfrequency seismic energy by determining a scaling
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factor between the observed peak amplitudes (from
the MSA at 240 s), and the moment magnitudes of
the corresponding earthquakes (Mw > 6.0), as listed
in the Harvard CMT catalog [Dziewonski and
Woodhouse, 1983].
[37] Since we know the location of both the
array and each earthquake, as well as the event
origin time, we can calculate the theoretical onset
time of the R1 train at the center of the array
and select only those peaks that correspond to
the arrival time of the R1 train. However, the
selection of R1 peaks is made difficult by the
presence of secondary peaks corresponding to
later arriving Rayleigh wave trains from the
previous larger earthquakes (R2,R3. . .). When
such secondary peaks are present, the corresponding
seismic amplitude is significantly larger than
estimated, on average, based on the magnitude
of the earthquake considered. When estimating
the scaling factor, and to reduce contamination
due to large previous events, we therefore discard
those peaks from the data set that have relatively
high amplitude for a given magnitude level. This
means that, when applying this scaling factor,
our estimate of the hum level is maximum
(Figures A1a and A1b). Since we ignore the
effects of geometrical spreading, attenuation during propagation, as well as radiation pattern, this
is a very crude estimate. However, the estimated
noise background level is consistent with what
has been previously reported (Figures A1c and
A1d) from the analysis of free oscillation data
(e.g., Mw 5.75 [Ekström, 2001]; M 6.0 [Tanimoto
and Um, 1999]).
Acknowledgments
[38] We wish to thank the staff of BDSN, F-net, JMA, NOAA
for providing high-quality and continuous seismic and ocean
buoy data. We thank Spahr Webb and an anonymous reviewer
for helpful comments. Berkeley Seismological Laboratory
contribution 06-10.
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